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Five samples of a material were tested in a structure, and the interior temperatures (℃) reported...

Five samples of a material were tested in a structure, and the interior temperatures (℃) reported were as follows: 23.1, 22.4, 22.8, 22.6, 22.8. Test the hypothesis ?0: ? = 22.4 versus ??: ? > 22.4, using ? = 0.05.

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Homework Answers

Answer #1

H0: = 22.4

Ha: > 22.4

From Given sample data,

= 22.74 , S = 0.2608

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 22.74 - 22.4 ) / ( 0.2608 / √(5) )
t = 2.92

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)
Critical value t(α, n-1) = t(0.05 , 5-1) = 2.132

t > t(α, n-1) = 2.9151 > 2.132

Result :- Reject null hypothesis

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